EcoModder Forum What is the relationship between acceleration and fuel economy?

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 09-12-2017, 10:31 PM #1 (permalink) EcoModding Lurker   Join Date: Sep 2017 Location: Adrienne224 Posts: 1 Thanks: 20 Thanked 0 Times in 0 Posts What is the relationship between acceleration and fuel economy? I'm taking calculus I. How do I relate this question to calculus? I have a vague idea of what the relationship is but not regarding calculus if there is one. Thank you for your help.
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I would have to think for quite awhile to figure an answer, but maybe this will help. Acceleration is the anti-derivative of torque and BSFC charts might help relate it to fuel consumption.

Good Luck, Matt

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 09-13-2017, 10:30 AM #3 (permalink) Master EcoModder     Join Date: Feb 2011 Location: Phillips, WI Posts: 944 Nameless - '06 GMC Canyon 90 day: 37.06 mpg (US) Thanks: 180 Thanked 371 Times in 239 Posts Start by looking at two cases: Case 1: Assume a constant low acceleration to a speed. You reach that speed at a distance. Use the engine BSFC chart, gear ratios, and rear axle ratio to find fuel used. Case 2: Assume a constant high acceleration to the same speed, then constant speed to the same distance as Case 1. Use the engine BSFC chart, gear ratios, and rear axle ratio to find fuel used. Note that the engine efficiency (BSFC) varies with RPM and throttle opening. The variable engine efficiency is outside the scope of calculus I, so this problem cannot be solved using calculus I math. It would be a good problem for a class in numerical analysis, though. And good luck with your calculus class. Calculus II and III are even more fun! __________________ The vacuum gauge plus wheel covers helped increase summer 2015 mileage to 38.5 MPG, while summer 2016 mileage was 38.6 MPG without the wheel covers. Drove 10,708.4 miles in 2017 at 35.5 MPG.
 The Following 2 Users Say Thank You to JRMichler For This Useful Post: Ecky (09-13-2017), Xist (09-13-2017)
 09-13-2017, 11:06 AM #4 (permalink) Ecomuggler     Join Date: Jun 2012 Location: Mesa, AZ Posts: 6,406 Chorizo - '00 Honda Civic HX, baby! :D 90 day: 34.82 mpg (US) Mid-Life Crisis Fighter - '99 Honda Accord LX 90 day: 37.34 mpg (US) Thanks: 3,703 Thanked 1,149 Times in 859 Posts Calculus is one of the few classes I attempted at the community college (I took the rest with hundreds of my closest friends at the university) and I still could not manage it, so I was deprived of the additional fun of subsequent mathematics courses. Good luck learning a little bit more about how the universe works.
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The relationship between acceleration and fuel economy COULD look like a flattened bell curve, with very similar fuel economy through light-medium acceleration but worse economy at high acceleration and very low acceleration.

I hated calc 1, took me 3 tries to pass.

Which I proceeded to ventilate with an assortment of 7.62x54Rs, 9x19s, and 45 ACPs.

I keep the remains in my room, I want to hang it on the wall, but I haven't gotten around to it. I'll post a picture when I get back home.

Edit: Here it is.

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Isaac Newton

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Quote:
 Originally Posted by Daschicken Attachment 22667 Which I proceeded to ventilate with an assortment of 7.62x54Rs, 9x19s, and 45 ACPs. I keep the remains in my room, I want to hang it on the wall, but I haven't gotten around to it. I'll post a picture when I get back home. Edit: Here it is. Attachment 22670
About 20 years ago at work, I was visiting an engineer's office to chat with him about something.
He had a picture of "sir Isaac" on the wall above his desk. I pointed to the picture and asked him, "Isn't he the @\$\$h0le who invented calculus?"
We both had a good laugh over that.
The only dealing I've had with calculus since I earned my engineering degree has been getting it scraped off my teeth.

Back on topic...
Accelerating on a freeway on-ramp with my Mustang in 3rd gear (with the accelerator pedal about 1/2" from the floor to avoid open-loop-full-throttle enrichment), I get about 8 MPG instantaneous.
I shift @ 2500 RPM.
In 4th gear under the same conditions, I get around 10 MPG.
In 5th gear under the same conditions, I get around 15 MPG.
My average over the past 3 years is over 32 MPG.
How you accelerate doesn't affect your average fuel economy nearly as much as how you drive after you accelerate.
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Last edited by Mustang Dave; 09-15-2017 at 11:09 PM.. Reason: back on topic

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 09-16-2017, 12:03 AM #7 (permalink) Master EcoModder     Join Date: Oct 2009 Location: Red Deer, AB Posts: 417 Rondo - '07 Kia Rondo EX 90 day: 25.83 mpg (US) Tinkertoy2 - '00 Toyota Echo base Team Toyota 90 day: 46.03 mpg (US) Thanks: 37 Thanked 91 Times in 65 Posts I never got to take Calculus in school (maybe I didn't miss much). I don't know for sure if this will help, but I'm thinking an EV calculator like this one may help. EV Calculator Electricity is still a fuel but electric motors don't have as many variables, (pumping losses etc.) Torque curve is flatter. Hope it helps. __________________ Almost all my driving is done 1-5 miles at a time. Best short trip: 2.4 l/100 km, 3.9 km
 09-16-2017, 01:00 PM #8 (permalink) Master EcoModder   Join Date: Feb 2014 Location: Missoula, MT Posts: 1,394 Thanks: 94 Thanked 457 Times in 309 Posts 1/2 off topic, I was playing around with some hyperloop acceleration/deceleration/time at speed math and how long it would take to get different distances. Then I came across a post talking interstellar travel, constant acceleration, and relativity and my mind was blown again. I can never get enough trying to comprehend those kinds of speed and distances.
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Quote:
 Originally Posted by Adrienne224 I'm taking calculus I. How do I relate this question to calculus? I have a vague idea of what the relationship is but not regarding calculus if there is one. Thank you for your help.
I suspect the hardest part will probably converting the BSFC for a given engine into a purely mathematical formula that has a high enough correlation to the real BSFC of that engine .. Calculus needs the pure math formula to work with first .. You can't do calculus on the picture/graph 1st , you have to convert it to pure math 1st.

The rest is just combining all the relevant formulas .. and imputing all the variable data for a given engine , vehicle , environmental conditions ,etc.

At it's core .. acceleration is just the rate (power) at which some source of input energy (fuel) is being converted into kinetic energy of motion (minus all the sources of drag (Aero, Rolling, Gravity, etc) that are bleeding applied power/energy away).

The BSFC for given conditions tells you what the conversion efficiency is .. for fuel to shaft .. for any given rate of torque/force/RPM/Power/Energy .. that you need to achieve some desired rate of acceleration.
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 09-16-2017, 07:39 PM #10 (permalink) Ol' Skooler   Join Date: Jul 2009 Location: Tyler, TX Posts: 972 Beater Echo - '00 Toyota Echo Team Toyota 90 day: 42.67 mpg (US) Hondizzle - '97 Honda Civic DX Team Honda 90 day: 48.06 mpg (US) Thanks: 47 Thanked 131 Times in 109 Posts I was awright at calculus, no genius but able to keep up. Promptly forgot all that was taught afterwards. __________________ '97 Honda Civic DX Coupe 5MT '00 Echo - dead 2/17 '14 Chrysler Town + Country - the better half's car '67 Mustang Convertible - gone 1/17